1. Field of the Invention
The present invention relates to a phase-locked loop circuit (PLL) employing a gm-C VCO (voltage-controlled oscillator).
2. Description of the Related Art
In order to generate a cyclic signal having a stable frequency that is synchronous with a reference clock signal, a PLL circuit is employed. A typical PLL circuit includes a VCO (voltage-controlled oscillator), a divider, a phase comparator, and a loop filter. The VCO oscillates at a frequency that corresponds to an input control voltage. The divider divides the frequency of the output signal of the VCO by n. The phase comparator makes a comparison between the phase of the output signal of the VCO and the phase of the reference clock signal, and generates a phase difference signal which indicates the phase difference. The loop filter performs filtering of the phase difference signal, and generates a control voltage to be supplied to the VCO. The output signal of the VCO is output as a cyclic signal obtained by multiplying the frequency of the reference clock signal by n.
In some cases, such a PLL circuit employs a gm-C VCO. FIGS. 1A through 1D are circuit diagrams each showing a configuration of a gm-C VCO 10. FIG. 1A shows an overall configuration of the VCO 10. The gm-C VCO 10 includes a first amplifier 12, a second amplifier 14, and a gyrator 16. The first amplifier 12 has a transconductance gmOSC, and the second amplifier 14 has a transconductance gm.
FIG. 1B is a circuit diagram which shows a configuration of the gyrator 16. FIG. 1C is an equivalent circuit diagram showing a circuit obtained by simplifying the gyrator 16 into a single-ended circuit. The gyrator 16 includes a gm cell 18, a first capacitor C1, and a second capacitor C2. The gm cell 18 has a configuration including two gm amplifiers 18a and 18b arranged such that the input terminal of each amplifier is connected (cross-coupled) to the output terminal of the other amplifier. The gm amplifiers 18a and 18b have the same transconductance, which is taken as given to be α•gm. Here, α represents a coefficient. Furthermore, the first capacitor C1 and the second capacitor C2 are taken to have the same capacitance C.
The output current ic of the first gm amplifier is represented by Expression ic=α•gm•Vin. The second capacitor C2 is charged and discharged using the output current ic. Accordingly, the voltage VC of the capacitor C2 is represented by Expression Vc=α•gm•Vin/sC.
The output current iin of the gm amplifier 18b is represented by iin=α•gm•Vc=(α•gm)2•Vin/sC. Accordingly, the input impedance zin of the gyrator 16 is represented by zin=Vin/iin=s•C/(α•gm)2. That is to say, the gyrator 16 can be seen as equivalent to an inductance represented by L=C/(α•gm)2.
FIG. 1D shows an equivalent circuit diagram showing the VCO 10. The condition for oscillation required by the gm-C VCO 10 is represented by the following Expression (1).gmOSC>gm+1/Rgyrator  (1)
Here, Rgyrator represents the real part of the impedance of the gyrator 16.
By determining the transconductance of the first amplifier 12, i.e., gmOSC, and the transconductance of the second amplifier 14, i.e., gm, so as to satisfy Expression (1), the oscillation frequency fOSC of the VCO 10 is represented by the following Expression.fOSC=(α•gm+gmOSC−gm)/(2πC)  (2)
That is to say, the oscillation frequency fOSC receives the effects of the transconductance gmOSC of the first amplifier 12.
However, in some cases, depending on the usage of such a PLL circuit, there is a desire to oscillate such a VCO 10 at a frequency independent of the effects of the transconductance gmOSC of the first amplifier 12. In this case, the following relation should be satisfied.gmOSC=gm  (3)
In other words, the conductance of the first amplifier 12 and the second amplifier 14 as viewed from the gyrator 16 side, i.e., (gmOSC−gm), must be zero. That is to say, the first amplifier 12 and the second amplifier 14 must function as an open circuit as viewed from the gyrator 16 side. When Expression (3) is satisfied, the oscillation frequency fOSC of the VCO 10 is represented by the following Expression.fOSC=(α•gm)/(2πC)  (4)
That is to say, the oscillation frequency fOSC of the VCO 10 is determined by the ratio between the transconductance (α•gm) of the gyrator 16 and the capacitance C.
However, in a case in which the transconductance of the first amplifier 12, i.e., gmOSC, and the transconductance the second amplifier 14, i.e., gm, are determined so as to satisfy Expression (3), Expression (1) is not satisfied, leading to a problem in that such a gm-C VCO 10 cannot oscillate.